How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

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How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

Solution:

As per the question,

2 = No. of letters in automobile license plates

It is known that,

There are a total of 26 alphabets

Therefore, in the following number of ways, letter can be arranged without repetition,

$= 26 \times 25$

$=650$

3 = No. of digits in automobile license plates

It is known that, there are 10 digits

$\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \end{tabular}$

Therefore without repetitions the number of digits

$=10 \times 9 \times 8=720$

As a result, the total no. of way automobile license plates

$\begin{array}{l} =720 \times 650 \\ =468000 \end{array}$

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